Prolog

1
Prolog

• The language of logic

2
History

• Kowalski late 60s Logician who showed logical
  proof can support computation.
• Colmerauer early 70s Developed early version of
  Prolog for natural language processing, mainly
  multiple parses.
• Warren mid 70s First version of Prolog that was
  efficient.

3
Characteristics

• Prolog approximates first-order logic.
• Every program is a set of Horn clauses.
• Inference is by resolution.
• Search is by backtracking with unification.
• Basic data structure is term or tree.
• Variables are unknowns not locations.
• Prolog does not distinguish between inputs and
  outputs. It solves relations/predicates.

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SWI-Prolog Notes

• Free! Down Loadable
• To load a file
• consult( C\\kibler\\prolog\\test).
• For help
• help(predicate-name).
• will give you next solution.
• listing(member) will give definition.

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Example

• Facts ()
• likes(john,mary).
• likes(john,X). Variables begin with capital
• Queries
• ?- likes(X,Y).
• Xjohn, yMary. hit for more
• ?- likes(X,X).
• Xjohn.

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Example

• Rules
• likes(john,X) - likes(X,wine). - if
• likes(john,X)- female(X), likes(X,john).
• Note variables are dummy. Standarized apart
• Some Facts
• likes(bill,wine). female(mary). female(sue).
• Query ? - likes(john,Y).
• Y bill
• no.

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Family

• father(a,b).
• father(e,d).
• mother(c,b).
• mother(d,f).
• parent(X,Y) - father(X,Y).
• parent(X,Y) - mother(X,Y).
• grandfather(X,Y)- father(X,Z),parent(Z,Y).
• Do your own for practice.

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Informal Summary

• Program is facts rules. (horn clauses).
• Query conjunct of predicates.
• First set of bindings for variables that solve
  query are reported. If none, then Prolog returns
  no.
• Use to get other solutions.
• Can be viewed as constraint satisfaction program.

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MapColoring

• color(r). color(g). color(b).
• colormap(C1,C2,C3)-color(C1),color(C2),color(C3),
  C1\C2,
• C1\C3, C2\C3.
• Query colormap(X,Y,Z).
• X r, Y g, Zb.
• Is that it. Yes! Turn on trace.

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Unification (matching) terms

• Two terms UNIFY if there is a common substitution
  for all variables which makes them identical.
• f(g(X),Y) f(Z,Z). cheap unification
• X _G225, Yg(_G225).
• Look at parse tree for each term.
• variables match
• variable matches anything (set the binding)
• function symbols only match identical function
  symbols.

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Satisfiability uses unification

• sat(true). base case
• sat(not(false)). base case
• sat(or(X,Y))- sat(X).
• sat(or(X,Y))-sat(Y).
• sat(and(X,Y))-sat(X),sat(Y).
• test1(X,Y)- sat(and(not(X),X)).
• test2(X,Y)- sat(and(X,not(Y))).

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List Operator H T

• a,b,c is a list in Prolog.
• HT a,b,c results in
• H a i.e. the head of list
• T b,c i.e. the tail of the list.
• membership definition
• member(H,HT). base case first. Why?
• member(H,_T)- member(H,T).
• Use it.

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Member Tests

• ?- member(3,X).
• X 3 _G109. _G.., system generated
  variable
• X _G11,3 _. etc.
• ?- member(X,Y).
• X _G131, Y _G131, _G321.

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Permutation Insert

• insert(X,L, XL).
• insert(X,HT,HT1)- insert(X,T,T1).
• perm(,).
• perm(HT,P)-perm(T,T1),insert(H,T1,P).

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DFS

• solve(goal, solution Path)
• s(state, successor-state)
• dfs(N,N) - goal(N).
• dfs(N,NSol1)- s(N,N1), dfs(N1,Sol1).
• s(a,b). s(a,c). s(b,d). s(b,e). s(c,f).
• s(c,g). s(d,h). s(e,i). s(e,j). s(f,k).
• goal(i). goal(f).
• ?- dfs(a,N).
• N a, b, e, i
• N a, c, f

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Limitations

• 2nd order Cant ask what is relationship between
  heart and lungs?
• Probabilities What is likelihood of fire
  destroying Julian?